PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations
Conditions of Validity, Ch Series solutions, singular points and where the special functions come from
Problem
For y′′+x2+1y=0, a series solution is wanted about the ordinary point x=1 (not x=0).
((a)) Confirm that x=1 is an ordinary point.
((b)) Predict the radius within which that series is guaranteed to converge, using the distance in the complex plane from x=1 to the nearest singularity of the coefficient.